In recent years, as the flow in electric power systems becomes sophisticated, there has been a need to supply reliable, high-quality electric power. In particular, there has been an increasing need to improve the performance of an AC electric quantity measuring device in a three-phase circuit, a single-phase circuit, and an arbitrary multi-phase circuit that are essential in an electric power system control/protection device.
The present inventor has already proposed that an approach based on a rotation vector on a complex plane is useful to improve the performance in controlling and protecting an electric power system. This proposal is based on a basic approach in which AC voltage and current are expressed as vectors that rotate counterclockwise in a complex plane. For example, as described in Patent Document 1, the approach measures the voltages of an electric power system at timings obtained by evenly dividing one cycle of a reference wave by 4N (N is a positive integer), determines a voltage rotation vector the head of which has the voltage measured at a certain timing as the real-part coordinate and the voltage measured 90 degrees before as the imaginary-part coordinate, calculates the length of the chord connecting the head of the voltage rotation vector to the head of the preceding voltage rotation vector, determines an effective voltage from the voltages measured during the period from the certain timing to the timing one cycle of the reference wave before, and calculates the frequency of the electric power system from the phase angle of the voltage rotation vector calculated based on the sum of the chord lengths and the effective voltage. In Non-Patent Document 1, which presents a variety of equations for calculating AC electric quantities, a rated frequency of a system (50 or 60 Hz) is used to calculate AC electric quantities. In the present technology, when the frequency of the system deviates from the rated frequency, the frequency of the system is corrected in accordance with a frequency-gain characteristic curve or a fundamental wave is extracted in accordance with Fourier transform. In either case, a long computation time is required or the result has a large error.
FIG. 3 is a voltage rotation vector diagram expressed on a complex plane, where an instantaneous voltage v of an electric power system rotates counterclockwise around the origin O on the complex plane. The one-cycle period of a reference wave is divided into 4N portions (N is an integer), and the incremental period per step T is (60 Hz-system, 30-electrical-degree sampling (12 points/cycle sampling), T=1/60/12=0.00138889 seconds, for example). The rotation phase angle per step can be calculated as follows:
                              δ          ⁡                      (            t            )                          =                  2          ⁢                                          ⁢                      sin                          -              1                                ⁢                      {                                                            V                  2                                ⁡                                  (                  t                  )                                                            2                ⁢                                  V                  ⁡                                      (                    t                    )                                                                        }                                              (        1        )            
In the equation, V(t) represents the amplitude of the voltage, and V2(t) represents the length of the chord that subtends the rotation phase angle.
It is assumed that the amplitude and the chord length are obtained by performing integral operation on one-cycle instantaneous value data. The frequency is then calculated by the following equation:
                              f          ⁡                      (            t            )                          =                                                            ψ                ⁡                                  (                  t                  )                                                            2                ⁢                                                                  ⁢                π                                      ⁢                          f              0                                =                                                    4                ⁢                                  N                  ·                                      δ                    ⁡                                          (                      t                      )                                                                                                  2                ⁢                                                                  ⁢                π                                      ⁢                          f              0                                                          (        2        )            
In the equation, ψ(t) represents the one-cycle rotation phase angle of the voltage rotation vector, and f0 represents the reference wave frequency (50 or 60 Hz).
However, since phase variation due to voltage flickering or other produces errors in the voltage amplitude and the chord length, the frequency measurement result obtained from the equation (2) also contains a certain error. As described above, the equation (2) represents what is called a static frequency measuring method, which provides good measurement accuracy in a stationary state (sinusoidal wave), whereas inevitably producing an error when the phase varies, for example, due to voltage flickering. A method for addressing the problem that has been typically practiced in the present technology involves averaging frequency measurement results for an extended period (averaging processing) to remove the influence of voltage flickering. Such a frequency measuring device cannot therefore measure the frequency in real time, which poses a problem in high-speed, high-accuracy AC electric quantity measurement.    Patent Document 1: JP-A-2004-361124    Patent Document 2: WO-PCT/JP2007/052967    Non-Patent Document 1: “Development of Integral Method for Measuring RMS Active and Reactive Power in Single- and Multiphase Networks,” pp. 250-255, CEPSI 2002, Fukuoka, Japan